Solve for $x$ and $y$ using elimination. ${-2x-5y = -24}$ ${2x-2y = -4}$
We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $-2x$ and $2x$ cancel out. $-7y = -28$ $\dfrac{-7y}{{-7}} = \dfrac{-28}{{-7}}$ ${y = 4}$ Now that you know ${y = 4}$ , plug it back into $\thinspace {-2x-5y = -24}\thinspace$ to find $x$ ${-2x - 5}{(4)}{= -24}$ $-2x-20 = -24$ $-2x-20{+20} = -24{+20}$ $-2x = -4$ $\dfrac{-2x}{{-2}} = \dfrac{-4}{{-2}}$ ${x = 2}$ You can also plug ${y = 4}$ into $\thinspace {2x-2y = -4}\thinspace$ and get the same answer for $x$ : ${2x - 2}{(4)}{= -4}$ ${x = 2}$